三角函数的积化和差和差化积公式 三角函数积化和差，和差化积公式
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sinx+siny=2sin[(x+y)/2]cos[(x-y)/2]
sinx-siny=2cos[(x+y)/2]sin[(x-y)/2]
cosx+cosy=2cos[(x+y)/2]cos[(x-y)/2]
cosx-cosy=-2sin[(x+y)/2]sin[(x-y)/2]
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sinxsiny=-1/2[cos(x+y)-cos(x-y)]
cosxcosy=1/2[cos(x+y)+cos(x-y)]
sinxcosy=1/2[sin(x+y)+sin(x-y)]
cosxsiny=1/2[sin(x+y)-sin(x-y)]
cos(α+β)=cosαcosβ-sinαsinβ cos(α-β)=cosαcosβ+sinαsinβ sin(α+β)=sinαcosβ+cosαsinβ sin(α-β)=sinαcosβ -cosαsinβ
积化和差
sinαsinβ = [cos(α-β)-cos(α+β)] /2 cosαcosβ = [cos(α+β)+cos(α-β)]/2 sinαcosβ = [sin(α+β)+sin(α-β)]/2 cosαsinβ = [sin(α+β)-sin(α-β)]/2
和差化积：sinθ-sinφ=2cos(θ/2+φ/2)sin(θ/2-φ/2)
cosθ+cosφ=2cos(θ/2+φ/2)cos(θ/2-φ/2)
cosθ-cosφ=-2sin(θ/2+φ/2)sin(θ/2-φ/2)
积化和差：sinαsinβ=-[cos(α+β)-cos(α-β)]/2
cosαcosβ=[cos(α+β)+cos(α-β)]/2
sinαcosβ=[sin(α+β)+sin(α-β)]/2
cosαsinβ=[sin(α+β)-sin(α-β)]/2
和差化积：sinθ-sinφ=2cos(θ/2 φ/2)sin(θ/2-φ/2)
cosθ cosφ=2cos(θ/2 φ/2)cos(θ/2-φ/2)
cosθ-cosφ=-2sin(θ/2 φ/2)sin(θ/2-φ/2)
积化和差：sinαsinβ=-[cos(α β)-cos(α-β)]/2
cosαcosβ=[cos(α β) cos(α-β)]/2
sinαcosβ=[sin(α β) sin(α-β)]/2
cosαsinβ=[sin(α β)-sin(α-β)]/2
fgth
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